TAILIEUCHUNG - Doctor of philosophy in mathematics: Shortest paths along a sequence of line segments and connected orthogonal convex hulls

In the dissertation, we consider the problem of finding the shortest path between two points along a sequence of adjacent triangles in a general setting. The sequence of triangles is replaced by a sequence of ordered line segments. The 3D space is replaced by a Euclidean space. | VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY INSTITUTE OF MATHEMATICS PHONG THI THU HUYEN SHORTEST PATHS ALONG A SEQUENCE OF LINE SEGMENTS AND CONNECTED ORTHOGONAL CONVEX HULLS DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS HANOI - 2021 VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY INSTITUTE OF MATHEMATICS PHONG THI THU HUYEN SHORTEST PATHS ALONG A SEQUENCE OF LINE SEGMENTS AND CONNECTED ORTHOGONAL CONVEX HULLS Speciality Applied Mathematics Speciality code 9 46 01 12 DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS Supervisor Associate Professor PHAN THANH AN HANOI - 2021 Confirmation This dissertation was written on the basis of my research works carried out at Institute of Mathematics Vietnam Academy of Science and Technology un- der the supervision of Associate Professor Phan Thanh An. All the presented results have never been published by others. September 17 2021 The author Phong Thi Thu Huyen i Acknowledgment First and foremost I would like to thank my academic advisor Associate Professor Phan Thanh An for his guidance and constant encouragement. The wonderful research environment of the Institute of Mathematics Viet- nam Academy of Science and Technology and the excellence of its staff have helped me to complete this work within the schedule. I would like to express my special appreciation to Professor Hoang Xuan Phu Professor Nguyen Dong Yen Associate Professor Ta Duy Phuong and other members of the weekly seminar at Department of Numerical Analysis and Scientific Com- puting Institute of Mathematics as well as all the members of Associate Professor Phan Thanh An s research group for their valuable comments and suggestions on my research results. In particular I would like to express my sincere thanks to Associate Professor Nguyen Ngoc Hai and PhD student Nguyen Thi Le for their significant comments and suggestions .

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